Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solutions

TL;DR

This paper derives a finite Larmor radius approximation from the Vlasov equation under strong magnetic fields, and proves existence and uniqueness of certain stationary solutions depending on the magnetic field direction.

Contribution

It introduces a new finite Larmor radius model from classical plasma physics equations and establishes mathematical existence and uniqueness results for specific stationary solutions.

Findings

Finite Larmor radius approximation derived from Vlasov equation.

Existence and uniqueness of stationary solutions proven.

Heuristic derivation of the electroneutrality equation in this setting.

Abstract

A finite Larmor radius approximation is derived from the classical Vlasov equation, in the limit of large (and uniform) external magnetic field. We also provide an heuristic derivation of the electroneutrality equation in the finite Larmor radius setting. Existence and uniqueness of a solution is proven in the stationary frame for solutions depending only on the direction parallel to the magnetic field and factorizing in the velocity variables.